Well, unless the city uses chloramines instead of chlorine. It's easy for there to be a mistake about this. Sometimes the city website or information may be out of date and still say they use chlorine when in fact their lab has switched to adding chloramines to the tap water. Chloramines will stick around for quite a long time, killing bacteria. So unless you are quite certain (actually speaking to an authoritative lab person for instance) I would take the inexpensive precaution of using a good conditioner product.